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What's the minimum (physics first) to get an oscillator?

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IanB:

--- Quote from: RoGeorge on May 24, 2023, 09:00:24 am ---So, if I try to translate 2nd derivative in words, would it be correct to say an oscillator needs some sort of acceleration in its behavior?
--- End quote ---
Yes, but more precisely momentum, or transformation of energy between kinetic (relating to movement) and potential (relating to position) forms.


--- Quote ---If yes, then a rotating disk would also be an oscillator.
--- End quote ---
No, if it is simply rotating freely on a spindle. Yes, if it involves energy transformations between movement and position (a balance wheel in a watch).


--- Quote ---This might still be OK (saying "might" because just like ejeffrey, I'm tempted to think circular motion is not the same as an oscillator), but the 2nd derivative condition doesn't make any good if, for example, it's a linear acceleration.  Something has to repeat, to be periodic, to alternate.  I don't see how the 2nd derivative implies alternation, or am I misunderstanding the 2nd derivative condition you were mentioning?
--- End quote ---
Yes, the second derivative enables alternation, but does not guarantee it (there can be overdamped systems).

A second order term is needed for oscillation, but not all second order systems will oscillate.


--- Quote ---To me, the problem of explaining something in terms of math is that there is no causality in an equation.  An equation is an equivalence, a relation between it's terms, and that can only be true or false.  It's like saying an oscillator is something that satisfy the oscillating conditions.  That would be a circular definition, same as saying an oscillator is an oscillator.
--- End quote ---
An equation if properly constructed is a mathematical model of a physical system. It replaces intuition with analysis, and enables predictions to be made about how the physical system will behave. If you write a good model of a system, you can tell if the system will oscillate.

bdunham7:

--- Quote from: IanB on May 24, 2023, 04:21:11 am ---Well, that would depend on how you wish to define oscillator.

--- End quote ---

Perhaps there the terms 'resonate' and 'oscillate' should be contrasted and compared here.  A relaxation oscillator seems to not quite fit some of the definitions of 'oscillator' that I'm seeing discussed here.  The only difference I can see between my proposed device and a relaxation oscillator is that the latter works by the accumulation of physical energy and the former accumulates a record of the energy.  You could redesign things so that each pip of the Geiger counter would add a small charge to a capacitor until a neon bulb discharges it.  Would that be different?


--- Quote ---It would seem more like a random number generator.

--- End quote ---

If it were a black box, how would you describe it based solely on it's output?

T3sl4co1l:

--- Quote from: IanB on May 24, 2023, 03:20:07 pm ---
--- Quote ---If yes, then a rotating disk would also be an oscillator.
--- End quote ---
No, if it is simply rotating freely on a spindle. Yes, if it involves energy transformations between movement and position (a balance wheel in a watch).

--- End quote ---

Why so chauvinistic about kinds of energy transformations? ;D

Free rotation being the exchange of linear kinetic energy between orthogonal axes.  The state variable and conjugate are position and position (or velocity or whatever).  It bears all the other hallmarks, like centripetal force implying energy storage (and indeed storing a little in the material elastically, though usually not enough to worry about).

I understand the feeling though. It seems too trivial or simple a form. :)

Tim

westfw:

--- Quote ---a rotating disk would also be an oscillator.
--- End quote ---
Certainly any point on the disk (except the center) appears to oscillate in nice sinusoids on any one-dimension axis.
I'm not sure how that ties in to the need for energy transfers... 

RJSV:
Dealing with low level logic,  the essential 'work horse' concept is the simple inverter, allowing for some complexity in the time domain, with certain hookups (or topography).
   So, skipping the complexities of integrals and differentials, is just a few logic gates, and time delays in propagation, AN OSCILLATOR can be had, and can be described, inside a 'paradox' structure.  For the particular paradox, being harnessed, your oscillator needs to be under two rules:
   #1.).   Output follows input logic level, with perhaps optional gain.
and
   "2.).  Input is generated by processing output through an inverter, where both signals are digital, or two state having thresholds for switching requirements.

    I think that's a logic defined oscillator, vs. the analog definitions seen in some replies here.

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